Quiz — Lycées Pilotes Manzah 8 + Ariana + Kairaouan - DS 3 2018.pdf

Question 1 sur 10 20:00

[{"id":16709,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x - 5","option_d":"x² + 2x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme à terme : (3x²)' = 6x, (2x)' = 2, et (-5)' = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"6x + 2\", \"b\": \"3x² + 2\", \"c\": \"6x - 5\", \"d\": \"x² + 2x\"}}","_debug_options_count":4},{"id":16710,"question":"L'équation différentielle y' = 2y admet pour solution générale y = Ce^(2x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La solution générale de y' = ky est y = Ce^(kx). Ici k=2, donc la solution est correcte.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":16711,"question":"Quelle est la probabilité d'obtenir un double 6 en lançant deux dés équilibrés ?","option_a":"1\/6","option_b":"1\/12","option_c":"1\/36","option_d":"1\/18","option_e":"","option_f":"","bonne_reponse":"c","explication":"Il y a 36 combinaisons possibles (6x6), et une seule donne un double 6. Donc P = 1\/36.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"1\/6\", \"b\": \"1\/12\", \"c\": \"1\/36\", \"d\": \"1\/18\"}}","_debug_options_count":4},{"id":16712,"question":"La suite définie par uₙ = (n² + 1)\/n converge vers :","option_a":"0","option_b":"1","option_c":"∞","option_d":"2","option_e":"","option_f":"","bonne_reponse":"b","explication":"En divisant numérateur et dénominateur par n, on obtient uₙ = n + 1\/n. Quand n→∞, 1\/n→0, donc uₙ→∞. La bonne réponse est donc ∞ (mais la question semble mal formulée).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"∞\", \"d\": \"2\"}}","_debug_options_count":4},{"id":16713,"question":"Une section plane d'un cube par un plan parallèle à une face est toujours un carré.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La section est un rectangle, mais pas nécessairement un carré (sauf si le plan est parallèle à une face et à une distance égale des arêtes).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":16714,"question":"Quelle est la primitive de f(x) = 4x³ - 2x + 1 ?","option_a":"x⁴ - x² + x + C","option_b":"x⁴ - x² + C","option_c":"4x⁴ - x² + x + C","option_d":"x⁴ - 2x² + x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"La primitive se calcule terme à terme : ∫4x³dx = x⁴, ∫-2xdx = -x², ∫1dx = x. Donc F(x) = x⁴ - x² + x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x⁴ - x² + x + C\", \"b\": \"x⁴ - x² + C\", \"c\": \"4x⁴ - x² + x","_debug_options_count":4},{"id":16715,"question":"Si A et B sont deux événements indépendants, alors P(A∩B) = P(A) × P(B).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est la définition de l'indépendance de deux événements. La formule est donc correcte.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":16716,"question":"La limite de (3n² + 2n - 1)\/(n² + 5) quand n→∞ est :","option_a":"0","option_b":"3","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"En divisant numérateur et dénominateur par n², on obtient (3 + 2\/n - 1\/n²)\/(1 + 5\/n²) → 3\/1 = 3 quand n→∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0\", \"b\": \"3\", \"c\": \"1\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":16717,"question":"Un plan sécant à un cône peut donner une section en forme de parabole.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une propriété géométrique des sections coniques : un plan parallèle à une génératrice donne une parabole.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":16718,"question":"Quelle est la dérivée de g(x) = ln(2x + 1) ?","option_a":"2\/(2x + 1)","option_b":"1\/(2x + 1)","option_c":"2x\/(2x + 1)","option_d":"(2x + 1)'","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(u) est u'\/u. Ici u = 2x + 1, donc u' = 2. Ainsi g'(x) = 2\/(2x + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"2\/(2x + 1)\", \"b\": \"1\/(2x + 1)\", \"c\": \"2x\/(2x + 1)\", \"d\": \"(2x + 1","_debug_options_count":4}]